Open AccessCLUSTER SIZE DISTRIBUTION IN THE n-POLYMER COAGULATION PROCESSES AND THE JOINT COAGULATION PROCESSES
Author(s) -
Xue Yu,
Kong Ling-Jiang,
Weng Jia-Qiang
Publication year - 1992
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.41.1406
Subject(s) - coagulation , kernel (algebra) , polymer , connection (principal bundle) , cluster (spacecraft) , cluster size , physics , distribution (mathematics) , materials science , joint (building) , combinatorics , thermodynamics , mathematics , mathematical physics , mathematical analysis , computer science , condensed matter physics , nuclear magnetic resonance , geometry , psychology , psychiatry , programming language , architectural engineering , electronic structure , engineering
We have considered coagulation processes containing n-polymer interactions by means of a generalized Smoluchovski's equation, which is solved as a monodisperseinitial-value problem to the kernel: K(i1,i2,…,in)=A sumfrom i=1 to n i1+B, K(i1,i2,…,in)=A sumfrom i=1 to n i1. According to the connection between model K(i1,i2,…,in)=A sumfrom i=1 to n i1+B and K(i1,i2,…,in)= S(i1)S(i2)…S(in)(S=Ak+B),we obtain the pre-gel solution of the latter model. We also study a kind of joint coagulation process containing two-polymer and three-polymer collisions with the kernel K2(i, j)=i+j and K3(i,j,k) = i+j+k and get the explicit expression of Cm(t). Finally, we discuss the long-term behavior of Cm(t), Which can be extented to the general case.